Question: Vanessa is 20 years younger than Christopher. Christopher and Vanessa first met 3 years ago. Twelve years ago, Christopher was 3 times as old as Vanessa. How old is Christopher now?
Solution: We can use the given information to write down two equations that describe the ages of Christopher and Vanessa. Let Christopher's current age be $c$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $c = v + 20$ Twelve years ago, Christopher was $c - 12$ years old, and Vanessa was $v - 12$ years old. The information in the second sentence can be expressed in the following equation: $c - 12 = 3(v - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to solve our first equation for $v$ and substitute it into our second equation. Solving our first equation for $v$ , we get: $v = c - 20$ . Substituting this into our second equation, we get the equation: $c - 12 = 3($ $(c - 20)$ $ -$ $ 12)$ which combines the information about $c$ from both of our original equations. Simplifying the right side of this equation, we get: $c - 12 = 3c - 96$ Solving for $c$ , we get: $2 c = 84$ $c = 42$.